RMST-based multiple contrast tests in general factorial designs

TL;DR

This paper develops and evaluates new statistical tests based on the restricted mean survival time (RMST) for factorial designs, addressing limitations of existing methods in survival analysis without assuming proportional hazards.

Contribution

It extends permutation and Wald-type tests for RMST to general factorial designs, introduces multiple testing procedures with dependence structure, and assesses their performance through simulations and real data.

Findings

Proposed tests control type I error in small samples.

Multiple tests improve power by considering dependence.

Simulation results demonstrate effectiveness of the methods.

Abstract

Several methods in survival analysis are based on the proportional hazards assumption. However, this assumption is very restrictive and often not justifiable in practice. Therefore, effect estimands that do not rely on the proportional hazards assumption are highly desirable in practical applications. One popular example for this is the restricted mean survival time (RMST). It is defined as the area under the survival curve up to a prespecified time point and, thus, summarizes the survival curve into a meaningful estimand. For two-sample comparisons based on the RMST, previous research found the inflation of the type I error of the asymptotic test for small samples and, therefore, a two-sample permutation test has already been developed. The first goal of the present paper is to further extend the permutation test for general factorial designs and general contrast hypotheses by considering a Wald-type test statistic and its asymptotic behavior. Additionally, a groupwise bootstrap approach is considered. Moreover, when a global test detects a significant difference by comparing the RMSTs of more than two groups, it is of interest which specific RMST differences cause the result. However, global tests do not provide this information. Therefore, multiple tests for the RMST are developed in a second step to infer several null hypotheses simultaneously. Hereby, the asymptotically exact dependence structure between the local test statistics is incorporated to gain more power. Finally, the small sample performance of the proposed global and multiple testing procedures is analyzed in simulations and illustrated in a real data example.